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A255132 Number of divisors of odd Catalan numbers (A038003).

%I A255132 #16 Nov 11 2024 01:58:31
%S A255132 1,1,2,8,96,2048,3145728,206158430208,27670116110564327424,
%T A255132 498460498419343452338927647605129216,
%U A255132 24991100464315816765228594460089760794425300959309994174606999552,336610107623104398583024455855523763248864803845734108839073897168302318415095310965480469919661369165797247714066432
%N A255132 Number of divisors of odd Catalan numbers (A038003).
%H A255132 Chai Wah Wu, <a href="/A255132/b255132.txt">Table of n, a(n) for n = 0..14</a>
%F A255132 a(n) = A000005(A038003(n)).
%e A255132 A038003(4) = 9694845 which has 96 divisors.
%o A255132 (Python)
%o A255132 from operator import mul
%o A255132 from functools import reduce
%o A255132 from sympy import factorint
%o A255132 A255132_list, c, s = [1, 1], {}, 3
%o A255132 for n in range(2,2**15):
%o A255132     for p,e in factorint(4*n-2).items():
%o A255132         if p in c:
%o A255132             c[p] += e
%o A255132         else:
%o A255132             c[p] = e
%o A255132     for p,e in factorint(n+1).items():
%o A255132         if c[p] == e:
%o A255132             del c[p]
%o A255132         else:
%o A255132             c[p] -= e
%o A255132     if n == s:
%o A255132         c2 = reduce(mul,[e+1 for e in c.values()])
%o A255132         A255132_list.append(c2)
%o A255132         s = 2*s+1
%Y A255132 Cf. A038003, A000005, A119861, A119908, A120274, A120275, A255133.
%K A255132 nonn
%O A255132 0,3
%A A255132 _Chai Wah Wu_, Feb 15 2015